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math.CO2026
Tree-cut decompositions for displaying undominated edge-ends
Max Pitz, Lucas Real
We prove that every graph admits a linked, componental, rooted tree-cut decomposition of finite adhesion that displays all undominated edge-ends. As a first application, we deduce…
math.CO2026
On tree-decompositions for infinite chordal graphs
Max Pitz, Lucas Real, Roman Schaut
A graph is chordal if it contains no induced cycle of length four or more. While finite chordal graphs are precisely those admitting tree-decompositions into cliques, this fails fo…
math.CO2026
On order-compatible paths in infinite graphs
Max Pitz, Lucas Real, Roman Schaut
Two paths in a graph are order-compatible if their common vertices occur in the same order when travelling from to . Suppose a graph contains an infinite number…